head 1.1; access; symbols; locks; strict; comment @# @; 1.1 date 2018.03.14.15.43.11; author root; state Exp; branches; next ; desc @This document (1.1 Midpoint Explorations) is re-created by administrator on 17 May 2017 @ 1.1 log @Initial revision @ text @{ "_id": { "$oid": "59425eaf4975ac013bf0f563" }, "_type": "GSystem", "access_policy": "PUBLIC", "altnames": "1.1 Midpoint Explorations", "annotations": [], "attribute_set": [], "author_set": [ 1 ], "collection_set": [], "comment_enabled": null, "content": "

GEOMETRIC REASONING

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Midpoint Explorations

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Task 1

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On the dot paper below, draw different squares. Join the midpoints of the sides of each of these squares (in order) to create a new quadrilateral. The first one is shown as an example.
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\r\nNOTE: The above activity can be done either on dot paper to be provided by school or on GeoGebra software installed on your computer
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\r\nObserve each of the new quadrilaterals formed, and complete the following:
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\r\nThe quadrilateral formed by joining the midpoints of  sides of a square is a ________
\r\n(Click here to write)

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\"Enter\"
\r\n\"me_U05A01Q01_en_img01\"

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Task 2\r\n\r\n
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Suppose you were to join the midpoints of sides of a rectangle in a similar fashion. What shape do you think you might get? Think about it, and write your conjecture here:
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The quadrilateral formed by joining the midpoints of sides of a  
\r\n___________________________________ is a   _________________________________
\r\n
\r\n(Click here to write)
\r\n\"Enter\"
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Task 3\r\n\r\n
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Now verify your conjecture by drawing different rectangles on the dot paper below and joining the midpoints of the sides.
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\r\nNOTE: The above activity can be done either on dot paper to be provided by school or on GeoGebra software installed on your computer
\r\n
\r\n\"me_U05A01Q03_en_img02\"

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Explain why you think your conjecture is true (or false)
\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

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Task 4\r\n\r\n
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Based on Task 3 does your conjecture hold? If not how would you modify it?

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(Click here to write)
\r\n\"Enter\"

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Task 5\r\n\r\n
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Now make similar conjectures about other special quadrilaterals - rhombus and parallelogram,  and verify them. Write your conjectures in the space provided, and use the dot grid for verifying. 

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NOTE: The above activity can be done either on dot paper to be provided by school or on GeoGebra software installed on your computer
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\r\n(Click here to write)
\r\n\"Enter\"
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\r\nConjecture 1:

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\r\n\u200b______________________________________________________________________________\r\n\r\n______________________________________________________________________________\r\n\r\n
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(Click here to write)
\r\n\"Enter\"
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\r\nConjecture 2:

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\r\n\u200b\u200b______________________________________________________________________________\r\n\r\n\u200b\u200b______________________________________________________________________________\r\n\"me_U05A01Q03_en_img02\"\r\n\r\n
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Task 6\r\n\r\n
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Drawing on your observations in the 5 previous tasks, make a conjecture about the shape formed by joining the midpoints of sides of any  quadrilateral.
\r\n(Click here to write)
\r\n\"Enter\"

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\r\n____________________________________________________________\r\n\r\n____________________________________________________________\r\n\r\n____________________________________________________________\r\n\r\n\"me_U05A01Q03_en_img02\"\r\n
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Extended Task: 1\r\n\r\n
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If possible, draw a quadrilateral, joining whose midpoints of sides in order gives a figure that is NOT a parallelogram. If not possible, explain why.
\r\n(Click here to write)
\r\n\"Enter\"

\r\n", "content_org": "
\r\nGEOMETRIC REASONING\r\n
\r\n\r\n

Midpoint Explorations

\r\n\r\n
\r\n

Task 1

\r\n\r\n
\r\n

On the dot paper below, draw different squares. Join the midpoints of the sides of each of these squares (in order) to create a new quadrilateral. The first one is shown as an example.
\r\n
\r\nObserve each of the new quadrilaterals formed, and complete the following:
\r\n
\r\nThe quadrilateral formed by joining the midpoints of  sides of a square is a ________
\r\n\"L11img1\"

\r\n\r\n
\r\n

Task 2

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\r\n

Suppose you were to join the midpoints of sides of a rectangle in a similar fashion. What shape do you think you might get? Think about it, and write your conjecture here:
\r\n 

\r\n\r\n

The quadrilateral formed by joining the midpoints of sides of a  
\r\n___________________________________ is a   _________________________________
\r\n
\r\n 

\r\n\r\n
\r\n

Task 3

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Now verify your conjecture by drawing different rectangles on the dot paper below and joining the midpoints of the sides.
\r\n\"L11img2\"

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\"Think\" Think about this!
\r\nExplain why you think your conjecture is true (or false)

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Task 4

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\r\nBased on Task 3 does your conjecture hold? If not how would you modify it?

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\r\n\u200b __________________________________________________________________________ \r\n __________________________________________________________________________\r\n\r\n\r\n
\r\n\r\n
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Task 5

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\r\nNow make similar conjectures about other special quadrilaterals - rhombus and parallelogram,  and verify them. Write your conjectures in the space provided, and use the dot grid for verifying. 
\r\n
\r\nConjecture 1:

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\r\n\u200b______________________________________________________________________________\r\n\r\n______________________________________________________________________________\r\n\r\n
\r\n\r\n

Conjecture 2:

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\r\n\u200b\u200b______________________________________________________________________________\r\n\r\n\u200b\u200b______________________________________________________________________________\r\n\"L11img2\"\r\n\r\n
\r\n\r\n
\r\n

Task 6

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Drawing on your observations in the 5 previous tasks, make a conjecture about the shape formed by joining the midpoints of sides of any  quadrilateral.
\r\n 

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\r\n____________________________________________________________\r\n\r\n____________________________________________________________\r\n\r\n____________________________________________________________\r\n\r\n\r\n
\r\n\r\n
\r\n

Extended Task: 1

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 \r\n

If possible, draw a quadrilateral, joining whose midpoints of sides in order gives a figure that is NOT a parallelogram. If not possible, explain why.

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